Question

Assign oxidation states to all of the atoms in each of the following: a. \(\mathrm{BiO}^{+}\) b. \(\mathrm{PO}_{4}^{3-}\) c. \(\mathrm{NO}_{2}^{-}\) d. \(\mathrm{Hg}_{2}^{2+}\)

Short answer

The oxidation states for the given chemical species are: a. Bi(+3), O(-2) b. P(+5), O(-2) c. N(+3), O(-2) d. Hg(+1) (for each Hg atom)

Step-by-step solution

Assign oxidation numbers to elements in their elemental states

In their elemental states, the oxidation number of all elements is zero. For this exercise, we don't have any elemental species, so we can move directly to the next step.

Use the known oxidation states of elements and the rules of oxidation numbers

a. For \(\mathrm{BiO}^{+}\): - Oxygen usually has an oxidation number of -2 in chemical compounds. - The compound has a total charge of +1. Let x be the oxidation number of Bi and apply the rule of charge balance: \[x - 2 = +1\] Solving for x, we get \(x = +3\), so the oxidation states are: Bi(+3), O(-2) b. For \(\mathrm{PO}_{4}^{3-}\): - Oxygen usually has an oxidation number of -2 in chemical compounds. - The compound has a total charge of -3. Let x be the oxidation number of P and apply the rule of charge balance: \[ x + 4(-2) = -3\] Solving for x, we get \(x = +5\), so the oxidation states are: P(+5), O(-2) c. For \(\mathrm{NO}_{2}^{-}\): - Oxygen usually has an oxidation number of -2 in chemical compounds. - The compound has a total charge of -1. Let x be the oxidation number of N and apply the rule of charge balance: \[ x + 2(-2) = -1\] Solving for x, we get \(x = +3\), so the oxidation states are: N(+3), O(-2) d. For \(\mathrm{Hg}_{2}^{2+}\): - The compound has a total charge of +2. - There are two Hg atoms in the species. Let x be the oxidation number of a single Hg atom and apply the rule of charge balance: \[ 2x = +2\] Solving for x, we get \(x = +1\), so the oxidation states are: Hg(+1) (for each Hg atom)

Key concepts

Oxidation Number Rules

Understanding oxidation numbers is fundamental in chemistry as they help predict how atoms interact in chemical reactions. These numbers indicate the degree of oxidation (loss of electrons) or reduction (gain of electrons) of an element in a compound or ion. Here are some rules to determine oxidation numbers:

• The oxidation number for any atom in its elemental form is zero. For instance, in \( ext{O}_2\), oxygen has an oxidation number of 0.
• In a compound, hydrogen usually has an oxidation number of +1, and oxygen usually has an oxidation number of -2.
• For monoatomic ions, the oxidation number equals the ion's charge. For example, in \( ext{Na}^+\), the oxidation number of \( ext{Na}\) is +1.
• The sum of oxidation numbers in a neutral compound must be zero. For example, in water (H₂O), the sum of oxidation numbers of hydrogen and oxygen adds up to zero.
• In polyatomic ions like \( ext{SO}_4^{2-}\), the sum of oxidation numbers equals the ionic charge. This is crucial in deriving the oxidation states of individual atoms within the ion.

By following these rules, one can systematically assign oxidation numbers to different atoms in compounds and ions.

Charge Balance

Understanding charge balance is essential to determining oxidation states in various chemical species. When analyzing a molecule or ion, the combined oxidation numbers must balance out to match the overall charge. To apply charge balance effectively: 1. **Identify the known oxidation states.** Typically, elements like oxygen and hydrogen have standard oxidation numbers of -2 and +1, respectively. 2. **Apply algebraic equations.** Use known oxidation numbers to set up an equation relating to the total charge of the compound or ion. This sometimes involves solving for unknown oxidation numbers (e.g., assigning 'x' to an unknown oxidation state in an equation). 3. **Calculate the unknown.** Adjust and solve for unknowns so that when added to known oxidation numbers, they give a sum equal to the total charge of the compound or ion. Using these steps, as shown in our example solutions, helps balance charges accurately, thereby determining precise oxidation numbers.

Chemical Compounds

Chemical compounds consist of two or more elements combined in specific ratios, bound by chemical forces. In understanding oxidation states, chemical compounds can be either neutral or charged. Here are basics everyone should know: - **Neutral Compounds:** These are compounds where the total charge is zero. For example, in water ( H₂O ), the combined oxidation numbers of hydrogen and oxygen are zero. - **Ionic Compounds:** Made of charged particles, usually involving metals and nonmetals, that form through electron transfer. For instance, sodium chloride (NaCl) is ionic with Na⁺ and Cl⁻ . - **Covalent Compounds:** Electrons are shared rather than transferred. Examples include methane ( CH₄ ). Understanding these distinctions in compounds aids in correctly determining the oxidation numbers, as the type of compound affects how electrons are shared or transferred, impacting oxidation states.

Oxidation Numbers in Ions

When working with ions, it is important to pay careful attention to how charge affects oxidation numbers. Polyatomic ions, which consist of many atoms, carry a net charge. Understanding how to assign oxidation numbers in these ions is crucial: - **Monoatomic Ions:** The oxidation number is simply the charge of the ion. For example, in Cl⁻ , the oxidation number of Cl is -1. - **Polyatomic Ions:** The sum of oxidation numbers must equal the overall charge of the ion. For instance, in the phosphate ion (PO₄³⁻), phosphorus has an oxidation number determined by balancing with oxygen’s typical -2 oxidation state, resulting in P having +5. - **Transition Metals in Ions:** Transition metals can have multiple oxidation states. Understanding their context within the ion is necessary to assign correct numbers. Often, the surrounding atoms or overall charge helps determine these states. By understanding oxidation numbers in ions, whether monoatomic or polyatomic, students learn to balance charges, which is crucial in predicting molecule and ionic behavior in reactions.